Properties of parallel lines cut by a transversal.pptx

transversal

1. Properties of parallel lines cut by a transversal

2. Activity 1: Name It A Recall Complete the table using the illustration below.

3. Parallelism: 1. Two lines are parallel if and only if they are coplanar and they do not intersect. (m || n)

4. 2. A line that intersects two or more lines at different points is called a transversal. a. The angles formed by the transversal with the two other lines are called: • exterior angles (∠1, ∠2, ∠7 and ∠8) • interior angles (∠3, ∠4, ∠5 and ∠6). b. The pairs of angles formed by the transversal with the other two lines are called:

5. • corresponding angles (∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8) • alternate-interior angles (∠3 and ∠6, ∠4 and ∠5) • alternate-exterior angles (∠1 and ∠8, ∠2 and ∠7) • interior angles on the same side of the transversal (∠3 and ∠5, ∠4 and ∠6) • exterior angles on the same side of the transversal (∠1 and ∠7, ∠2 and ∠8)

6. 3. If two lines are cut by a transversal, then the two lines are parallel if: a. corresponding angles are congruent. b. alternate-interior angles are congruent. c. alternate-exterior angles are congruent. d. interior angles on the same side of the transversal are supplementary. e. exterior angles on the same side of the transversal are supplementary.

7. Example 1: Lines p and q are cut by transversal r. Find the value of x make p ǁ q. ∠1 and ∠5 are alternate interior angles, m∠1 = 5x – 11 and m∠5 = 3x + 7. Solution: For the lines to be parallel, the given angles must be congruent. 5x – 11 = 3x + 7 2x = 18 x = 9

8. Example 2: Lines k and l are cut by transversal o ∠4 and ∠7 are same side interior angles, m∠4 = 6x + 3 and m∠7 = 4x + 7. Solution: For the lines to be parallel, the given angles must be supplementary. 6x + 3 + 4x + 7 = 180 10x + 10 = 180 10x = 170 x = 17